Estimation of tissue stiffness is an important means of noninvasive cancer detection. Existing elasticity reconstruction methods usually depend on a dense displacement field (given by ultrasound or MR images) and known external forces. Many imaging modalities, however, cannot provide details within an organ and therefore cannot provide such a displacement field. Furthermore, force exertion and measurement can be difficult for some internal organs, making boundary forces another missing parameter.
Material property estimation has been an important topic in noninvasive cancer diagnosis, since cancerous tissues tend to be stiffer than normal tissues. Traditional physical examination methods, such as palpation, are limited to detecting lesions close to the skin, and reproducible measurements are hard to achieve. With the advance of medical imaging technologies, it becomes possible to quantitatively study the material properties using noninvasive procedures.
Computer vision methods in combination with force or pressure sensing devices have been proposed to find material properties of tissues [1], [2]. These methods require a controlled environment in order to capture the video and force (pressure), and therefore the experiments are usually done ex vivo. Kauer et al. [1] combined the video and pressure capturing components into a single device to simplify the measurement process, so that it can be performed in vivo during a surgical intervention. However, the device still needs to be in direct contact with the tissue, and only a small portion of the tissue can be measured due to the size of the device.
Elasticity reconstruction, or elastography, is a noninvasive method for acquiring strain or stiffness images using known external forces and a known displacement field [3], [4]. The reconstruction is usually formulated as an inverse problem of a physically-based simulation of elastic bodies, and a popular choice of the simulator is based on a linear elasticity model solved with the finite element method (FEM) [5], where the domain of the image is subdivided into tetrahedrons or hexahedrons called elements, with vertices known as nodes. Boundary conditions (displacement vectors or forces) on some of the nodes must be given to drive the simulation. Under this framework, nodal displacement vectors need to be computed based on a pair of images, and the force exertion mechanism needs to be controlled so that external forces can be measured. Otherwise, without measured forces, only relative elasticity values can be recovered. Ultrasound elastography [6], for example, compares two ultrasound images, one taken at the rest pose, and the other taken when a known force is applied. The displacement vector for each pixel can be estimated using cross-correlation analysis [3], [7] or dynamic programming [8] to maximize the similarity of echo amplitude and displacement continuity. Alternatively, in dynamic elastography (for example, magnetic resonance elastography (MRE) and vibroelastography), an MRI or ultrasound machine in tune with an applied mechanical vibration (shear wave) is used to find the displacement field [4], [9]. With known external forces and displacement field, the elasticity can be computed by solving a least-squares problem [10], [11], [12], if the algebraic equations resulting from the physical model is linear. A real-time performance has been reported using this direct method with a simplified 2D domain that assumes homogeneous material within a region [12]. Another type of method uses iterative optimization to minimize the error in the displacement field generated by the simulator [13], [14], [15]. Although slower than directly solving the inverse problem, this type of method does not assume linearity of the underlying physical model. A different kind of elastography [16], [17], [18] maximizes image similarity without requiring the displacement field or boundary conditions to be known, but the method relies on salient features within the object (such as the breast), which may not be present in CT images of organs such as the prostate. A phantom study applied the method to the prostate [17], but the model and boundary conditions are greatly simplified, and their method has not been applied to real patient data. A Bayesian framework has also been proposed to solve the elastography problem without requiring known boundary conditions [19]. That method, however, depends on assumptions about probability distribution functions and extensive sampling in a very high dimensional parameter space (elasticity and boundary conditions), which significantly limits the number of boundary nodes. While these methods are instrumental in their respective fields of interest, they are less well suited for a more general, multi-organ case where the image intensity may be almost constant within an organ, such as the prostate, and the lack of image details within the object makes it impossible to rely on pixel-wise correspondence. Moreover, the force exertion or vibration actuation mechanism can become complicated when the target tissues are deep inside the body. For example, for an elastography of the prostate, an actuator or a pressure sensor is sometimes inserted into the urethra or the rectum [20], [9], [21].
Elasticity parameters are also essential in cardiac function estimation, where sequential data assimilation [22], [23] has been applied to estimate simulation parameters and displacements simultaneously for dynamic mechanical systems. The parameters and observations of displacements (states) at each time step are modeled with a probability distribution, and a filtering procedure is applied over some time to estimate the states. Due to the computational complexity of the method, the number of estimated parameters has been very limited in work on cardiac function estimation [22]. On the other hand, our parameter space includes external forces as well as the Young's modulus, and the displacement field cannot be acquired directly from some common imaging modality like CT.
Accordingly, there exists a need for the ability to estimate biological tissue elasticity parameters where either the force or displacement is unknown or cannot be determined. Specifically, there exists a need for non-invasive estimation of biological tissue elasticity parameters and use of same for non-invasive cancer detection and cancer staging.